As a window into quantum gravity, a black hole is second only to the Big Bang, I suppose...

Shortly after the beginning, vacuum energy was cruel enough to put spacetime on the Rack, stretching it beyond recognition. But near the end, gravitational energy is beyond cruel to toss space and time into a taffy machine, turning it into a gooey mess!

So to pick your window into quantum gravity is to pick your torture into it, I'm afraid...

Your mug seems somewhat similar to the KITP mugs that, when filled with hot water, reveal a map of the CMB. My office-mate currently has one sitting on his desk, and I'm pretty sure David Gross also uses one.